In [36]: 
from IPython.display import Image
Image(filename='split/sdgmn3_1.png')
Out[36]:




The Python scripts for all the computations displayed here are available at:







https://github.com/mboudour/GraphMultilayerity










In [37]:





Image(filename='split/sdgmn3_2.png')
















    Out[37]:

























In [38]:





Image(filename='split/sdgmn3_3.png')
















    Out[38]:

























In [39]:





Image(filename='split/sdgmn3_4.png')
















    Out[39]:

























In [40]:





Image(filename='split/sdgmn3_5.png')
















    Out[40]:






















A Sierpinski (Fractal) Self-Similar Graph










In [41]:





%matplotlib inline
















In [42]:





run SierpinskiCantorGraph.py








































In [43]:





Image(filename='split/sdgmn3_6.png')
















    Out[43]:

























In [44]:





Image(filename='split/sdgmn3_7.png')
















    Out[44]:

























In [45]:





Image(filename='split/sdgmn3_8.png')
















    Out[45]:

























EXAMPLES
 
 1. Synthetic 3-Layer Graphs in the Triangular Topology
 2. Synthetic 3-Layer Graphs in the 2-Path Topology
 3. Analytic 3-Layer Graphs in the Triangular Topology
 4. Analytic 3-Layer Graphs in the 2-Path Topology
 5. Temporal Graphs with 3 Slices
 
 






 1. Synthetic 3-Layer Graphs in the Triangular Topology










In [46]:





%matplotlib inline
from syntheticThreeLayerGraph import synthetic_three_level, plot_graph

n1=n2=n3=50
p1=p2=p3=0.01
q1=q2=q3=0.01

G,J,FF,DD,edgeList = synthetic_three_level(n1,n2,n3,p1,p2,p3,q1,q2,q3,no_isolates=False)
pos=plot_graph(G,J,FF,DD,n1,n2,n3,d1=1,d2=10.,d3=0.8,nodesize=50,withlabels=False,edgelist=edgeList,layout=False,b_alpha=0.25)








































In [47]:





from threeLayerCommunityParition import create_node_comm_graph, plot_graph

broken_graph,broken_partition,npartition = create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [48]:





from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph

broken_graph,broken_partition,npartition = create_node_conncomp_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [49]:





from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph

r1=r2=r3=0.333

broken_graph,broken_partition,npartition = create_node_3attri_graph(G,J.nodes(),FF.nodes(),DD.nodes(),r1,r2,r3)
plot_graph(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)





































 2. Synthetic 3-Layer Graphs in the 2-Path Topology










In [50]:





from syntheticThreeLayerGraph_l import synthetic_three_level, plot_graph

n1=n2=n3=50
p1=p2=p3=0.01
q1=q2=q3=0.01

G,J,FF,DD,edgeList = synthetic_three_level(n1,n2,n3,p1,p2,p3,q1,q2,q3,no_isolates=False)
pos=plot_graph(G,J,FF,DD,n1,n2,n3,d1=2,d2=3.,nodesize=50,withlabels=False,edgelist=edgeList,layout=False,b_alpha=0.25)








































In [51]:





from threeLayerCommunityParition import create_node_comm_graph, plot_graph_stack

broken_graph,broken_partition,npartition = create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [52]:





from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph_stack

broken_graph,broken_partition,npartition = create_node_conncomp_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [53]:





from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph_stack

r1=r2=r3=0.333

broken_graph,broken_partition,npartition = create_node_3attri_graph(G,J.nodes(),FF.nodes(),DD.nodes(),r1,r2,r3)
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)





































 3. Analytic 3-Layer Graphs in the Triangular Topology










In [54]:





from analyticThreeLayerGraph import analyticThreeLayerGraph, plot_graph

n = 150
p = 0.01
r1 = r2 = r3 = 0.333

G, layer1, layer2, layer3, edgeList = analyticThreeLayerGraph(n,p,r1,r2,r3,G_isolates=True)
plot_graph(G,layer1,layer2,layer3,d1=1.5,d2=5.,d3=0.8,nodesize=100,withlabels=False,edgelist=edgeList,layout=False,alpha=0.25)








































In [55]:





from threeLayerCommunityParition import create_node_comm_graph, plot_graph

broken_graph,broken_partition,npartition = create_node_comm_graph(G,layer1,layer2,layer3)
plot_graph(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [56]:





from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph

broken_graph,broken_partition,npartition = create_node_conncomp_graph(G,layer1,layer2,layer3)
plot_graph(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [57]:





from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph

r1=r2=r3=0.333

broken_graph,broken_partition,npartition = create_node_3attri_graph(G,layer1,layer2,layer3,r1,r2,r3)
plot_graph(G,broken_graph,broken_partition,npartition,layer1,layer2,layer3,d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)





































 4. Analytic 3-Layer Graphs in the 2-Path Topology










In [58]:





from analyticThreeLayerGraph_l import analyticThreeLayerGraph, plot_graph

n = 150
p = 0.01
r1 = 0.333
r2 = 0.333
r3 = 0.333

G, layer1, layer2, layer3, edgeList = analyticThreeLayerGraph(n,p,r1,r2,r3,G_isolates=True)
plot_graph(G,layer1,layer2,layer3,d1=3.5,d2=5.,d3=0.8,nodesize=100,withlabels=False,edgelist=edgeList,layout=False,alpha=0.2)








































In [59]:





from threeLayerCommunityParition import create_node_comm_graph, plot_graph_stack

broken_graph,broken_partition,npartition = create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [60]:





from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph_stack

broken_graph,broken_partition,npartition = create_node_conncomp_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [61]:





from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph_stack

r1=r2=r3=0.333

broken_graph,broken_partition,npartition = create_node_3attri_graph(G,J.nodes(),FF.nodes(),DD.nodes(),r1,r2,r3)
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)





































 5. Temporal Graph with 3 Slices










In [62]:





%matplotlib inline
from syntheticThreeLayerGraph_time import synthetic_three_level, plot_graph

p1=p2=p3=0.1
n=50
G,J,FF,DD,JFD,edgeList = synthetic_three_level(n,p1,p2,p3,J_isolates=True,F_isolates=True,D_isolates=True)
#print edgeList
created_pos=plot_graph(n,G,J,FF,DD,JFD,d1=2.,d2=3.,nodesize=50,withlabels=False,edgelist=edgeList,layout=False,b_alpha=0.05) #d=0.5 #d








































In [63]:





from threeLayerCommunityParition import create_node_comm_graph, plot_graph_stack

broken_graph,broken_partition,npartition = create_node_comm_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [64]:





from threeLayerConnComponentsPartition import create_node_conncomp_graph, plot_graph_stack

broken_graph,broken_partition,npartition = create_node_conncomp_graph(G,J.nodes(),FF.nodes(),DD.nodes())
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)








































In [65]:





from threeLayer3AttributesPartition import create_node_3attri_graph, plot_graph_stack

r1=r2=r3=0.333

broken_graph,broken_partition,npartition = create_node_3attri_graph(G,J.nodes(),FF.nodes(),DD.nodes(),r1,r2,r3)
plot_graph_stack(G,broken_graph,broken_partition,npartition,J.nodes(),FF.nodes(),DD.nodes(),d1=1.4,d2=5.,d3=0.8,withlabels=False,nodesize=100,layout=False)